To solve the equation, we need to isolate x on one side of the equation. Subtracting 5 from both sides, we get: $$x + 5 - 5 = 12 - 5$$ $$x = 7$$

The area of a rectangle is calculated by multiplying its length and width. Therefore, the area of the given rectangle is: $$Area = length \times width$$ $$Area = 8 cm \times 5 cm$$ $$Area = 40 cm^2$$

To simplify the expression, we can distribute the negative sign to the terms inside the second parentheses: $$(3x + 2y) - (2x - 3y)$$ $$3x + 2y - 2x + 3y$$ Combining like terms, we get: $$x + 5y$$

To solve the proportion, we can cross-multiply: $$x \times 6 = 3 \times 4$$ $$6x = 12$$ Dividing both sides by 6, we get: $$x = \frac{12}{6}$$ $$x = 2$$

The volume of a cube is calculated by cubing its side length. Therefore, the volume of the given cube is: $$Volume = side^3$$ $$Volume = 4 cm^3$$ $$Volume = 64 cm^3$$

To solve the inequality, we need to isolate x on one side of the inequality sign. Adding 5 to both sides, we get: $$2x - 5 + 5 < 13 + 5$$ $$2x < 18$$ Dividing both sides by 2, we get: $$x < \frac{18}{2}$$ $$x < 9$$

The slope of a line passing through two points $$ (x_1, y_1) $$ and $$ (x_2, y_2) $$ is given by the formula: $$m = \frac{y_2 - y_1}{x_2 - x_1}$$ Substituting the given points, we get: $$m = \frac{7 - 3}{5 - 2}$$ $$m = \frac{4}{3}$$

Simplifying the expression, we get: $$\sqrt{16} + \sqrt{49} - \sqrt{25}$$ $$4 + 7 - 5$$ $$14$$

The perimeter of a triangle is the sum of the lengths of its sides. Therefore, the perimeter of the given triangle is: $$Perimeter = 6 cm + 8 cm + 10 cm$$ $$Perimeter = 24 cm$$

To solve the equation, we need to isolate x on one side of the equation. Distributing the 3 to the terms inside the parentheses, we get: $$3x - 6 = 15$$ Adding 6 to both sides, we get: $$3x - 6 + 6 = 15 + 6$$ $$3x = 21$$ Dividing both sides by 3, we get: $$x = \frac{21}{3}$$ $$x = 7$$

The area of a circle is calculated using the formula: $$Area = \pi r^2$$ Substituting the given radius, we get: $$Area = \pi \times 7^2$$ $$Area = \pi \times 49$$ $$Area = 154 cm^2$$

To simplify the expression, we can use polynomial long division: $$rac{x^2 + 2x + 1}{x + 1} = x + 1$$ The remainder is 0, which means that the expression simplifies to $$x + 1$$. Therefore, the answer is $$x + 1$$.

To solve the equation, we need to isolate y on one side of the equation. Subtracting 5 from both sides, we get: $$2y + 5 - 5 = 17 - 5$$ $$2y = 12$$ Dividing both sides by 2, we get: $$y = \frac{12}{2}$$ $$y = 6$$

When flipping a coin, there are two possible outcomes: head or tail. Since both outcomes are equally likely, the probability of getting a head is 1/2.

The volume of a cylinder is calculated using the formula: $$Volume = \pi r^2 h$$ Substituting the given radius and height, we get: $$Volume = \pi \times 5^2 \times 10$$ $$Volume = \pi \times 25 \times 10$$ $$Volume = 250 cm^3$$